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C3×D5525 #45684127

order33150
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5525
unambiguous semidirect productC17⋊(C3×D325)
unambiguous semidirect productC25⋊(C3×D221)

Splittings

Fitting, HallC3×C13×C17×C25 ⋊ C2
derived, HallC13×C17×C25 ⋊ C2×C3
HallC3×C17×C25 ⋊ D13
HallC3×C13×C25 ⋊ D17
HallC3×C13×C17 ⋊ D25
HallC17×C25 ⋊ C3×D13
HallC13×C25 ⋊ C3×D17
HallC13×C17 ⋊ C3×D25
HallC3×C25 ⋊ D221
HallC3×C17 ⋊ D325
HallC3×C13 ⋊ D425
SylowC25 ⋊ C3×D221
SylowC17 ⋊ C3×D325
SylowC13 ⋊ C3×D425

Subgroups

subgroupG/H
center, hypercenterC3D5525
commutator, cosocle, hypocenterC13×C17×C25C2×C3
FrattiniC5C3×D1105
FittingC3×C13×C17×C25C2
socleC3×C5×C13×C17D5
LCSG ▷ C13×C17×C25
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 16575

A minimal faithful permutation representation — 2 generators on 58 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41)(42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

8292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 9);